Skip to main content

Application of Modified Couple Stress Theory and Homotopy Perturbation Method in Investigation of Electromechanical Behaviors of Carbon Nanotubes

  • Mir Masoud Seyyed Fakhrabadi (a1)

The paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method. Due to the less accuracy of the classical elasticity theorems, the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes. Both of the static and dynamic behaviors under static DC and step DC voltages are discussed. The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.

Corresponding author
*Corresponding author. Email:, (M. M. S. Fakhrabadi)
Hide All
[1] Iijima S., Helical microtubules of graphitic carbon, Nature, 354(6348) (1991), pp. 5658.
[2] Sung M., Paek S.-U., Ahn S.-H. and Lee J. H., A study of carbon-nanotube-based nanoelectromechanical resonators tuned by shear strain, Comput. Mater. Sci., 51(1) (2012), pp. 360364.
[3] Loh O., Wei X., Sullivan J., Ocola L. E., Divan R. and Espinosa H. D., Carbon-carbon contacts for robust nanoelectromechanical switches, Adv. Mater., 24(18) (2012), pp. 24632468.
[4] Cheng C. L. and Zhao G. J., Steered molecular dynamics simulation study on dynamic self-assembly of single-stranded DNA with double-walled carbon nanotube and graphene, Nanoscale, 4(7) (2012), pp. 23012305.
[5] Adhikari S. and Chowdhury R., The calibration of carbon nanotube based bionanosensors, J. Appl. Phys., 107(12) (2010), pp. 124322124322.
[6] Koochi A., Kazemi A. S., Noghrehabadi A., Yekrangi A. and Abadyan M., New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets, Mater. Design, 32(5) (2011), pp. 29492955.
[7] Fakhrabadi M. M. S., Samadzadeh M., Rastgoo A., Yazdi M. H. and Mashhadi M. M., Vibrational analysis of carbon nanotubes using molecular mechanics and artificial neural network, Physica E: Low-Dimensional Systems and Nanostructures, 44(3) (2011), pp. 565578.
[8] Fakhrabadi M. M. S., Amini A., Reshadi F., Khani N. and Rastgoo A., Investigation of buckling and vibration properties of hetero-junctioned and coiled carbon nanotubes, Comput. Mater. Sci., 73 (2013), pp. 93112.
[9] Huang X., Yuan H., Liang W. and Zhang S., Mechanical properties and deformation morphologies of covalently bridged multi-walled carbon nanotubes: multiscale modeling, J. Mech. Phys. Solids, 58(11) (2010), pp. 18471862.
[10] Pradhan S. C. and Murmu T., Small-scale effect on vibration analysis of single-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory, J. Appl. Phys., 105(12) (2009), pp. 124306124306.
[11] Ansola R., Veguería E., Canales J. and Alonso C., Evolutionary optimization of compliant mechanisms subjected to non-uniform thermal effects, J. Finite. Elements. Anal. Design, 57 (2012), pp. 114.
[12] Tayyaba S., Afzulpurkar N. and Ashraf M. W., Simulation and design optimization of piezoelectricaly actuated valveless blood pump for hemofiltration system, J. Sens. Transducers., 139 (2012), pp. 6378.
[13] Zand M. M., The dynamic pull-in instability and snap-through behavior of initially curved microbeams, J. Mech. Adv. Mat. Struct., 19 (2012), pp. 485491.
[14] Stölken J. S. and Evans A. G., A microbend test method for measuring the plasticity length scale, Acta Materialia, 46(14) (1998), pp. 51095115.
[15] Mindlin R. and Tiersten H., Effects of couple-stresses in linear elasticity, Archive Rat. Mech. Anal., 11(1) (1962), pp. 415448.
[16] Yang F., Chong A. C. M., Lam D. C. C. and Tong P., Couple stress based strain gradient theory for elasticity, Int. J. Solids Structures, 39(10) (2002), pp. 27312743.
[17] Koiter W. T., Couple stresses in the theory of elasticity, I and II, Nederl. Akad. Wetensch. Proc. Ser. B, 67 (1964), pp. 1729.
[18] Toupin R. A., Elastic materials with couple-stresses, Archive Rat. Mech. Anal., 11(1) (1962), pp. 385414.
[19] Mindlin R. D., Influence of couple-stresses on stress concentrations, Exp. Mech., 3(1) (1963), pp. 17.
[20] Mindlin R. D. and Tiersten H. F., Effects of couple-stresses in linear elasticity, Archive Rat. Mech. Anal., 11(1) (1962), pp. 415448.
[21] Dequesnes M., Rotkin S. V. and Aluru N. R., Calculation of pull-in voltages for nanoelectromechanical switches, J. Nanotech., 13 (2002), pp. 120131.
[22] Ke C. and Espinosa H. D., Numerical analysis of nanotube based NEMS devices–part I: electrostatic charge distribution on multiwalled nanotubes, J. Appl. Mech., 72 (2005), pp. 721725.
[23] Ke C., Espinosa H. D. and Pugno N., Numerical analysis of nanotube based NEMS devices– part II: role of finite kinematics, stretching and charge concentration, J. Appl.Mech., 72 (2005), pp. 726731.
[24] Ouakad H. M. and Younis M. I., Nonlinear dynamics of electrically actuated carbon nanotube resonators, J. Comput. Nonlinear Dyn., 5 (2010), pp. 113.
[25] Soroush R., Koochi A., Kazemi A. S., Noghrehabadi A., Haddadpour H. and Abadyan M., Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano actuators, J. Phys. Scr., 82 (2010), 045801.
[26] Koochi A., Kazemi A., Khandani F. and Abadyan M., Influence of surface effects on size-dependent instability of nano-actuators in the presence of quantum vacuum fluctuations, J. Phys. Scr., 85 (2012), 035804.
[27] Abadyan M., Novinzadeh A. and Kazemi A., Approximating the effect of the Casimir force on the instability of electrostatic nano-cantilevers, J. Phys. Scr., 81 (2010), 015801.
[28] Koochi A., Noghrehabadi A., Abadyan M. and Roohi E., Approximating the effect of van der Waals force on the instability of electrostatic nano-cantilevers, Int. J. Modern Phys. B, 25(29) (2011), pp. 39653976.
[29] Abdi J., Koochi A., Kazemi A. S. and Abadyan M., Modeling the effects of size dependence and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory, Smart Mater. Struct., 20 (2011), 055011.
[30] He J. H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178(3) (1999), pp. 257262.
[31] Yang F., Chong A. C. M., Lam D. C. C. and Tong P., Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39(10) (2002), pp. 27312743.
[32] Ke C. H., Pugno N., Peng B. and Espinosa H. D., Experiments and modeling of carbon nanotube-based NEMS devices, J. Mech. Phys. Solids, 53(6) (2005), pp. 13141333.
[33] Fakhrabadi M. M. S., Rastgoo A. and Ahmadian M. T., Analysis of pull-in instability of electrostatically actuated carbon nanotubes using the homotopy perturbation method, J. Mech. Mater. Struct., 8(8) (2013), pp. 385401.
[34] Mojahedi M., Zand M. M. and Ahmadian M. T., J. Appl. Math. Model., 34 (2010), pp. 10321041.
[35] Zand M. Moghimi and Ahmadian M. T., Application of homotopy analysis method in studying dynamic pull-in instability of microsystems, Mech. Res. Commun., 36(7) (2009), pp. 851858.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 95 *
Loading metrics...

Abstract views

Total abstract views: 549 *
Loading metrics...

* Views captured on Cambridge Core between 11th October 2016 - 21st January 2018. This data will be updated every 24 hours.